Mapping electrical crosstalk in pixelated sensor arrays

ABSTRACT

The effects of inter pixel capacitance in a pixilated array may be measured by first resetting all pixels in the array to a first voltage, where a first image is read out, followed by resetting only a subset of pixels in the array to a second voltage, where a second image is read out, where the difference in the first and second images provide information about the inter pixel capacitance. Other embodiments are described and claimed.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.12/009,959, filed on Jan. 18, 2008, and incorporated herein by referencein its entirety.

GOVERNMENT INTEREST

The invention claimed herein was made in the performance of work under aNASA contract, and is subject to the provisions of Public Law 96-517 (35USC 202) in which the Contractor has elected to retain title.

BACKGROUND

For some systems employing pixilated sensor arrays or MEMS(Micro-Electrical-Mechanical Systems) arrays, it is desirable to measurethe capacitance at each element (pixel) in the array. For example, thedetection of electromagnetic radiation comprises several steps,including photon capture, collection of photo-generated charges, andsensing the corresponding voltages. Capacitive coupling between pixelsmay induce errors in their corresponding sensed voltages, which may leadto inaccurate image values. This capacitive coupling may affect theelectronic gain and linearity of each pixel. Capacitive coupling causesthe photo-generated charge on a pixel to induce a voltage on one or moreadjacent or nearby pixels, leading to cross-talk when the voltages aresensed.

For some systems employing pixilated sensor arrays or MEMS(Micro-Electrical-Mechanical Systems) arrays, it is desirable to measurethe capacitance at each element (pixel) in the array. For example, thedetection of electromagnetic radiation comprises several steps,including photon capture, carrier diffusion, collection ofphoto-generated charges, and sensing the corresponding voltages.Capacitive coupling between pixels may induce errors in theircorresponding sensed voltages, which may lead to inaccurate imagevalues. This capacitive coupling may affect the electronic gain andlinearity of each pixel. Capacitive coupling causes the photo-generatedcharge on a pixel to induce a voltage on one or more adjacent or nearbypixels, leading to cross-talk in the sensed voltages in each pixel.

It is desirable to provide a map of capacitive coupling for all elementsin a pixelated array, which may be useful in calibration procedures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an array of pixels and controller according to anembodiment.

FIG. 2 illustrates a subset of pixels with associated cells and annuliaccording to an embodiment.

FIG. 3 illustrates a procedure according to an embodiment.

DESCRIPTION OF EMBODIMENTS

In the description that follows, the scope of the term “someembodiments” is not to be so limited as to mean more than oneembodiment, but rather, the scope may include one embodiment, more thanone embodiment, or perhaps all embodiments.

FIG. 1 illustrates a system according to an embodiment, where aprocedure for measuring capacitance coupling among pixels in array 102is carried out by control system 104 under instructions stored incomputer readable media (memory) 106. The procedure stored in computerreadable media 106 will be described later. Readout electronics 108 and110 read out the pixel voltages in array 102, as well as providingvarious control signals to array 102.

Depicted in pictorial form in FIG. 1 is a subset array of pixels,denoted by dashed rectangle 112. This subset is modeled, as indicated indashed rectangle 114, as a set of nodes, each one having a nodecapacitance to ground (substrate). A node with a capacitor to groundrepresents a pixel. The model of 114 indicates capacitive couplingbetween center pixel 115 and its four nearest neighbor pixels. The modelindicated by 114 is overly simplified because it does not explicitlyshow all pairs of coupling capacitors between the pixels, and does notshow capacitive coupling to pixels that are not nearest neighbors. Inpractice, there may be capacitive coupling between a pixel and itsnext-to-nearest neighboring pixels, as well as other pixels.

Pixel 115 is modeled at the circuit level within dashed rectangle 116.Pixel 116 comprises reset transistor 118, photodetector 120, andtransistor 122 configured as a source follower (buffer). The sourceterminal of transistor 122 is connected to other circuit components,such as a readout circuit, but for simplicity such a connection is notshown. The output voltage, V_(OUT), is taken at the source terminal oftransistor 122. When the reset voltage on the gate of transistor 118 isHIGH, transistor 118 is turned ON to provide a reset voltage tophotodetector 120, so that the capacitance of photodetector 120 ischarged. (In 114, the capacitance for photodetector 120 is shown as acapacitor from a node to ground.) After reset, transistor 118 is turnedOFF. During image capture, photons absorbed by photodetector 120 causeelectron-hole pairs, which discharge the capacitance. During readout,the output voltage V_(OUT) is indicative of this charge.

Pixels for other embodiments may be modeled differently than asillustrated in FIG. 1. That is, some embodiments may utilize pixels inwhich the model of FIG. 1 is not applicable, or where other models maybe more accurate.

Embodiments provide results indicative of capacitive coupling in asensor array by reading out all pixel voltages when each pixel in thearray has been reset to a first reset voltage, and by reading out allpixel voltages when a second reset voltage, different from the firstreset voltage, is used to reset only those pixels in a subset of thepixels in the array. The pixels not in the subset are reset to the firstreset voltage. During this procedure, it is not necessary that the arrayis sensing an applied image, so that the embodiments may be utilizedwhen the sensor array is kept dark. This procedure may be repeated forvarious subsets, so that for some embodiments each pixel would have hadan opportunity to be reset at the second reset voltage. Signalprocessing schemes may be applied to these pixel voltages to providemetrics indicative of the capacitive coupling.

To describe one or more embodiments in more detail, it is convenient toconsider that the pixels and their corresponding voltages in a sensorarray may be indexed according to their row and column numbers.Accordingly, let v₀(i,j) denote the output voltage of a pixel atposition (i, j) obtained from a readout when all pixels in the arrayhave been reset to voltage v₀; and let v₁(i,j) denote the output voltageof a pixel at position (i,j) obtained from a readout when all pixels butsome subset in the array have been reset to voltage v₀, and where thepixels in the subset have been reset to voltage v₁.

Suppose the index i ranges over the integer set {1, 2, . . . , N}, andthe index j ranges over the integer set {1, 2, . . . , M}. To make thenotation concise, these integer sets may be denoted as I and J,respectively. Accordingly, the set {v₀(i,j), iεI, jεJ} may be consideredan image, and likewise the set {v₁(i,j), iεI, jεJ} may be consideredanother image. An ensemble of such images may be accumulated so thataverage (or baseline) images may be provided. That is, for someembodiments, multiple readouts of the entire array of pixels are made toprovide an ensemble of voltages v₀(i,j) and v₁(i,j), followed byaveraging to provide an average of v₀(i,j) over the ensemble and anaverage of v₁(i,j) over the ensemble. Additional notation could be addedto v₀(i,j) and v₁(i,j) to denote their averages, but for ease ofpresentation such additional notation will not be introduced. In lightof this, it should be noted that when considering the description below,that for some embodiments, v₀(i,j) and v₁(i,j) may represent averagesover an ensemble of measurements.

A difference v₁(i,j)−v₀(i,j) may be calculated for each index pair (i,j)to provide a set of differences. This set of differences, which may betermed a difference image, is indicative of the capacitive couplingbetween pixels, and may depend upon the particular choice of subset ofpixels that were reset to the voltage v₁. It is convenient to denotethis dependence by introducing s to represent a subset of pixels. Thedifference d(i,j,s)=v₁(i,j)−v₀(i,j) may then be calculated for each pair(i,j) for some subset s. This gives a set of differences Δ(s)={d(i,j,s),iεI, jεJ}. A family of such sets may be provided by performing theabove-described procedure for a family of subsets. The family of subsetsmay be chosen to cover the entire array.

As a particular example, a subset may be chosen such that each pixel inthe subset is separated from its nearest neighbor by 6 pixels. That is,we might choose a subset comprising pixels at positions {(i,j), i=1, 7,14, 21, . . . ; j=1, 7, 14, 21, . . . }. There will be edge effects, sofor simplicity assume that N and M are multiples of 7. This subset maybe denoted as s₁. Another subset may be chosen by shifting this subsetby one position, either in a row direction or a column direction, unlessof course the edge of the array has already been bumped into. Forexample; a second subset may be the set of positions {(i,j), i=2, 8, 15,22, . . . ; j=1, 7, 14, 21, . . . }. This subset may be denoted as s₂.This process may be repeated, each time shifting a subset to obtain anew subset, so that the family of all subsets covers the entire array.

In the absence of a gradient in either the first or second resetvoltages across the imager, or alternatively, in the presence of anidentical gradient in both the first and second reset voltages, thevoltage coupling for each pixel may be directly determined from thedifference image, Δ(s)={d(i,j, s), iεI, jεJ}. For the ideal case inwhich there is no capacitive coupling, the image would only have thedifference voltage for the pixels that had the second reset voltageapplied. If coupling is present, then this difference image willdirectly give the sum of the coupling voltages from all couplinginteractions, in pixels surrounding the reset pixel. Thus, there is notonly the effect of the reset pixel on the nearest neighbor pixels, butalso the sum of the change in the nearest neighbors and the centralreset pixel on the next-nearest-neighbor, and vice versa.

There may be embodiments for which a gradient in the first reset imageis not cancelled out by the second reset image, or vice versa. If thegradient is in voltage only, the resulting image still gives thevoltage-to-voltage coupling accurately, but at voltage differences thatcorrespond to the gradient. If the gradient is in the illumination, thenthe voltage-to-voltage coupling may be analyzed by an iterative solutionthat uses the preferred electronic gain calculation to convert thegradient in illumination to a voltage, followed by calculating theinduced coupling, and then re-calculating the correct electronic gain,per pixel. This procedure may be repeated until convergence is achieved.This latter approach should also be performed if there is significantnon-linearity in the output voltage of the pixels, relative to the twopixel values in the before and after images.

For some embodiments, the set Δ(s)={d(i,j,s), iεI, jεJ} may be processedto mitigate effects due to local spatial variation in the array. Forsome embodiments, this procedure may be described as follows. The arraymay be divided into a contiguous family of cells, each cell being acontiguous set of pixels that includes one and only one pixel belongingto the subset s. That is, there is a one-to-one correspondence betweenthe pixels in the set s and the set of cells. Except near the edges ofthe array, for some embodiments the center of a cell may be the pixel inthat cell belonging to s. Generally, given a pixel position (k,l) thatbelongs to the subset s, the cell associated with (k,l) are those (i,j)for which the distance between (k,l) and (i,j) is less than or equal tothe distance between (i,j) and any other pixel in the subset s. FIG. 2illustrates this, where the dots in array 201 represent a portion of thesubset of pixels s that are reset to v₁. The dashed lines divide thearray into cells. (Not all cells are shown.)

About each pixel belonging to the subset s, a locus of pixels may bedefined, where the locus is inside the cell associated with the pixel.For example, locus 202 is drawn around pixel 204 in FIG. 2. Of course,the locus is not continuous, but is meant to represent the set of pixelswithin a cell that are at some given distance from the pixel in the cellbelonging to the subset s. For cells near the edge, the correspondinglocus may be truncated by the edge.

For any pixel position (i,j), there is one and only one cell containing(i,j), and that cell contains a pixel position that also belongs to thesubset s. Denote this pixel position as (i*, j*). (It depends also uponthe choice of subset s.) Note that if the pixel position (i,j) belongsto the subset s, then i*=i and j*=j. For the particular example in FIG.2, (i*,j*) is in the center of the shown cells. For the cell containing(i,j), an average over the locus associated with that cell may becalculated. More specifically, for any pixel position (i,j), letα(i*,j*,s) denote the average of the values d(m,n,s) on the locus ofpoints (m, n) associated with the cell containing (i,j). With thisnotation in mind, some embodiments provide the values

${\hat{d}\left( {i,j,s} \right)} = {\frac{{d\left( {i,j,s} \right)} - {a\left( {i^{*},j^{*},s} \right)}}{{d\left( {i^{*},j^{*},s} \right)} - {a\left( {i^{*},j^{*},s} \right)}}.}$Note that {circumflex over (d)}(i,j, s) is normalized to be less than orequal to one, and that {circumflex over (d)}(i*,j*,s)=1.

For each subset s, the set {circumflex over (Δ)}(s)={{circumflex over(d)}(i,j,s), IεI, jεJ} may be calculated as discussed above.Furthermore, a family of these sets may be calculated for a family ofsubsets s that cover the array. This family of sets may provideinformation about the capacitive coupling among pixels in an array, andto what degree capacitive coupling is important as a function of intrapixel distance. For example, for a particular subset s, all {circumflexover (d)}(i,j,s) for which (i,j) and (i*,j*) are nearest neighborsprovides information about the capacitive coupling among nearestneighbors; all {circumflex over (d)}(i,j,s) for which (i,j) and (i*,j*)are next-to-nearest neighbors provides information about the capacitivecoupling among next-to-nearest neighbors; and so forth. As a result,histograms may be generated based upon this family of sets, yieldinginformation about the degree of capacitive coupling. For some arrays,such histograms may show that capacitive coupling is not important forsufficiently large intra pixel distance. For example, for someembodiments, capacitive coupling has been found to be important only fornearest neighbors.

Some embodiments may provide a voltage-to-voltage coupling factor fornext neighbors and next-to-nearest neighbors. For example, for a regulartwo dimensional array (ignoring edge effects), pixel (i,j) has fournearest neighbors, pixels (i−1,j), (i+1,j), (i,j−1), and (i,j+1), andfour next-to-nearest neighbors, pixels (i−1,j−1), (i+1,j−1), (i−1,j+1),and (i+1,j+1). Let k and l denote relative pixel index values such thatd_(i,j)(k,l,s) references voltage differences for the nearest andnext-to-nearest neighbors to pixel (i,j). That is, the (k, l) indexpairs (−1,0), (1,0), (0,−1), and (0,1) delineate the nearest neighborsto pixel (i,j), and the (k, l) index pairs (−1,−1), (−1,1), (1,−1), and(1,1) delineate the next-to-nearest neighbors to pixel (i,j). With thisnotation, some embodiments may provide coupling factors D_(i,j)(k,l,s)where

${D_{i,j}\left( {k,l,s} \right)} = {\frac{d_{i,j}\left( {k,l,s} \right)}{d\left( {i,j,s} \right)}.}$Clearly, this scheme may be extended for all n^(th)-nearest neighboringpixels for all pixels (i,j) in an array, with appropriate truncation atthe edges of the array.

One may obtain ratios for the coupling capacitors, relative to theiradjacent diode capacitors, for the pixel array of interest using the setof coupling factors, even for the general case where all of the diodecapacitances and all of the coupling capacitances are assumed to varyamong each other. One may use iterative algorithms (e.g. simulatedannealing) to independently calculate the capacitance values. There maybe simpler algorithms (e.g. perturbation methods) for more restrictedassumptions, such as for the assumption of equal diode capacitances andequal coupling capacitances. An imager average nodal capacitance may beavailable from conversion gain measurements. Deviations of diodecapacitance values may be small, relative to the average, and couplingcapacitance values may be small, relative to the diode capacitances.

One may obtain ratios for the coupling capacitors, relative to theiradjacent diode capacitors, even for the general case where all of thediode capacitances and all of the coupling capacitances are assumed tovary among each other. One may use iterative algorithms (e.g. simulatedannealing) to independently calculate the capacitance values. There maybe simpler algorithms (e.g. perturbation methods) for more restrictedassumptions, such as for the assumption of equal diode capacitances andequal coupling capacitances. An imager average nodal capacitance may beavailable from conversion gain measurements. Deviations of diodecapacitance values may be small, relative to the average, and couplingcapacitance values may be small, relative to the diode capacitances.

Green's function methods or matrix inversion methods may be used tocalculate both diode and coupling capacitances under more constrainedexperimental conditions, such as for example a uniform flat field, onlysingle pixel reset, and uniformity of all coupling capacitances, andseparately, uniformity of all diode capacitances. Separate kernels maybe used to obtain the corresponding charge-to-voltage coupling factors.

Various modifications may be made to the disclosed embodiments withoutdeparting from the scope of the invention as claimed below. For example,instead of setting all the pixels to the first voltage v₀ beforeselectively setting a subset to the second voltage v₁, for someembodiments a flat field may be imaged so that all the pixels accumulatea first charge g₀. For such embodiments, one may perform an iterativeanalysis where to calculate an implied voltage coupling, calculate theimplied capacitance correction, then perform a localized backgroundsubtraction to remove illumination non-uniformities, and thenre-calculate the voltage coupling until convergence of the calculatedcoupling value. Furthermore, for some embodiments, instead of settingthe subset of pixels to the second voltage v₁, a beam spot may be usedto illuminate only the pixels in the subset, one at a time, or apatterned beam may be used to evenly illuminate the pixels in thesubset, more than one at a time so that the subset accumulates a secondcharge q₁. Similar remarks as discussed with respect to analysis for theflat field also apply to the analysis of the subset of pixels.

Furthermore, some embodiments may not utilize a flat illumination field,and for some embodiments, the subset of pixels need not be a regularspaced sub-array.

Some of these procedures are illustrated in the flow diagram of FIG. 3,where in process 302 all the pixels are set to the first voltage v₀, orin the case of a different procedural mode, all the pixels are insteadilluminated with a flat field so that all the pixels accumulate thefirst charge g₀. In process 304, the image is acquired. In process 306,some pre-selected subset of the pixels in the array are set to thesecond voltage v₁, or in the case of a different procedural mode, thepixels in this subset are instead illuminated to accumulate the secondcharge q₁. In process 308, a new image is acquired, and a differenceimage is formed by taking the difference between the previously acquiredimage and the new image. In process 310, the subset of pixels isshifted, as discussed earlier, and control is brought back to process302. The procedure stops when the family of all subsets has covered thearray.

Throughout the description of the embodiments, various mathematicalrelationships are used to describe relationships among one or morequantities. For example, a mathematical relationship or mathematicaltransformation may express a relationship by which a quantity is derivedfrom one or more other quantities by way of various mathematicaloperations, such as addition, subtraction, multiplication, division,etc. Or, a mathematical relationship may indicate that a quantity islarger, smaller, or equal to another quantity. These relationships andtransformations are in practice not satisfied exactly, and shouldtherefore be interpreted as “designed for” relationships andtransformations. One of ordinary skill in the art may design variousworking embodiments to satisfy various mathematical relationships ortransformations, but these relationships or transformations can only bemet within the tolerances of the technology available to thepractitioner.

Accordingly, in the following claims, it is to be understood thatclaimed mathematical relationships or transformations can in practiceonly be met within the tolerances or precision of the technologyavailable to the practitioner, and that the scope of the claimed subjectmatter includes those embodiments that substantially satisfy themathematical relationships or transformations so claimed.

What is claimed is:
 1. A system comprising: an array of pixels, eachpixel operating substantially at a same wavelength; and a controllercoupled to the array of pixels, the controller configured to: acquire afirst image based on illuminating each pixel in the array to accumulatea first charge; acquire a second image based on illuminating only thosepixels in a subset of the array to accumulate a second charge, thesubset being less than an entirety of pixels in the array of pixels andcomprising pixels spaced two or more pixel-distance apart; and form adifference image based on the first and second images.
 2. The system asset forth in claim 1, the controller configured to acquire a firstfamily of images based on illuminating each pixel in the array toaccumulate the first charge and acquire a second family of images basedon illuminating only those pixels in a subset of the array to accumulatea second charge.
 3. The system as set forth in claim 2, where the familyof subsets covers the array.
 4. The system as set forth in claim 1,wherein the first image is based on an average of voltage readouts bythe controller based on illuminating each pixel in the array toaccumulate the first charge, and the second image is based on an averageof voltage readouts by the controller based on illuminating only thosepixels in a subset of the array to accumulate the second charge.
 5. Thesystem as set forth in claim 1, wherein the subset comprisesnext-nearest neighbor pixels.
 6. The system as set forth in claim 2,wherein the controller is further configured to acquire each image ofthe second family of images based on illuminating a different subset ofpixels for each image of the second family of images.
 7. The system asset forth in claim 6, wherein the controller is further configured toacquire one image of the second family of images based on illuminatingnearest-neighbor pixels in a first subset, and another image of thesecond family of images based on illuminating next-nearest-neighborpixels in a second subset.
 8. The system as set forth in claim 6,wherein the controller is further configured to acquire one image of thesecond family of images based on illuminating pixels in a first subset,the pixels in the first subset being spaced six pixel-distance apart. 9.The system as set forth in claim 1, wherein the controller is furtherconfigured to: acquire a plurality of additional images based onilluminating only those pixels in additional subsets of the array toaccumulate a second charge, the subset being less than an entirety ofpixels in the array of pixels and comprising pixels spaced two or morepixel-distance apart; and form a plurality of difference images eachbased on a difference between the first and each of the additionalimages, wherein each additional subset is different from otheradditional subsets.
 10. The system as set forth in claim 1, wherein thecontroller is further configured to calculate a capacitance of eachpixel of the array of pixels, based on the difference image.
 11. Thesystem as set forth in claim 9, wherein the controller is furtherconfigured to calculate a capacitance of each pixel of the array ofpixels, based on the plurality of difference images.